The diameter of a biscuit is approximately 51 millimeters (mm). An atom of bismuth (Bi) is approximately 320. picometers (pm) in diameter. Calculate the number of bismuth atoms needed to span the diameter of a biscuit in a line. Express your answer in scientific notation, showing the correct number of significant figures. (Enter your answer using one of the following formats: 1.2e-3 for 0.0012 and 1.20e+2 for 120.

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Answer:

Bismuth atoms = 1,59375e+8

Step-by-step explanation:

Data: Biscuit diameter = 51 mm

         Bismuth (Bi) atom diameter = 320 pm

We need to calculate the number of bismuth atoms needed to span the diameter of a biscuit in a line. First we need to choose a unit to work with. In this case i'm going to use picometers.

We transform the biscuit diameter to picometer by using a rule of three:

1 mm = 1e+9 pm ⇒ 51 mm = 5,1e+10 pm

[tex]\frac{1 mm}{51 mm}=\frac{1e+9 pm}{x}[/tex]  

x = 5,1e+10 pm

Remember that:

1 m = 1e+12 pm

1 cm = 1e+10 pm

1 mm = 1e+9 pm

Now we calculate how many Bismuth atoms we need to span the diameter of a biscuit in a line:

[tex]Bismuth atoms = \frac{5,1e+10 pm}{320 pm}\\ Bismuth atoms = 1,59375e+8[/tex]